Just some things i'd check (along with the already good suggestions).
- I know this has been mentioned but arcing plug caps (40 yr old ones) seems to be a common problem. I had #2 only staying cold and it was by only checking it at night that i could tell that the cap was gone (external arcing). I temporarily cleaned the plug cap & wrapped it with electrical tape (with several layers) and it stopped arcing and the cylinder was firing properly again. This was a temporary fix so i could move onto other things. I've sinced replaced them with new caps and that completely solved that.
If that spark plug is coming out wet, then you are getting fuel which is a good sign (but that doesn't gaurantee the idle circuit is working correctly so that would still need to be checked as 'steam-powered man' suggested). As already mentioned replace that plug & check for excessive carbon/sootyness (or other uncleaniness which could be deep down in the plug!) as this could be causing misfiring & keeping the cylinder cold due to shorting within the plug instead of sparking at the gap. If replacing or cleaning the plug still doesn't fix it, check your leads for continuity/discontinuity.
When checking leads, you can do a 'lead' to 'lead' check. Since you know that it is only one cylinder thats getting cold (& not two cylinders that are shared 1.4 or 2.3), this tells you that your coil is fine, but doesn't rule out a problem with one of the leads. So, unscrew the plug caps so they are removed and no longer part of the equation, and check the lead-to-lead resistance with a multimeter by inserting each multimeter probe into the end of each lead. If both leads are ok, you will be effectively reading the resistance of the secondary winding of the coil (see pic) which should be around 14K ohms. Here i'm refering to checking between points 'A' and 'B' on the picture. If you want to test between cap-to-cap (by not unscrewing them), then you should get around (10K + 10K + 14K) = 34K ohms reading. This is between points 'C' and 'D' on the picture. So this is a end-to-end test for the coil & leads/caps in question. The resistance values i've mentioned assumes stock coils & stock plug caps, not after market ones.
- Other things carb related (already mentioned). Check that the float levels are set correctly and that the needle and seat is also operating correctly. If you have a chance to have the carbs on the bench, you can test by blowing through the fuel tube that the needle and seat is operating like a ON/OFF switch upon contact as the float is moved up and down, and whilst blocking the other carb needle and seat. You can also do this on the the bike, by removing the shared fuel line (as it comes from the tank and runs to the respective "T" peice of the two carb set). Remove the relevant fuel line from the petcock, and remove the 2 fuel bowls shared by the line you just took off. I.e. Either bowls for (#1 & #2) carbs or bowls for (#3 & #4) carbs. Lets say #2 is staying cold, then with one hand hold #1 fuel float upwards to block it off, & simultaneously blow through the hose to see if #2 needle & seat hisses air when you let it rest down, & that it also blocks the air when you hold it up. The hissing should be ON/OFF and also should actuate at the point of correct float height, so you can measure that too (on the bike). Petrol tastes great don't it
NOT. Alright, cup your hand over the fuel line and blow into your hand (ahh you dirty minds).
Before doing the above, you can first try gently & firmly tapping the fuel bowl with the handle of a large screwdriver and see if it comes to life first before taking things off. I.e. in an attempt to unstick things in that carb.
- Make sure you have ample fuel in the tank (& the screen is clear in the petcock). More fuel in tank equals more pressure & gets fuel in the lines & to the carbs quicker. If everything is clean in the fuel tap/petcock/screen and fuel lines, then even a low fuel level will work fine, just might take a bit longer to fill the bowls.
- Check the routing of the fuel lines. Make sure they are like a "U" between the fuel tap and the T peices on the carbs.
- If you suspect that you are not getting fuel, another trick is to remove the airbox, then rev up the motor to get it breathing, then very quickly (& in one motion), close the throttle and cup your hand over the carb opening for the suspect carb (completely starving it for air), then crack the throttle open again to give it a few revs. This has the effect of pulling any debris from the orifices of the carbs (I.e. jets, etc) and sucking that through under higher vacuum (since your've now cut off the air). If its only a minor obstruction, then this might solve your problem and clean some carb issues up on the cheap. If you have a serious obstruction, then only a carb clean will do. I used to do this on cars all the time with success.
